Question

Calculate the perimeter and area of a quadrant of the circle whose radii are
i) $98$ cm
ii) $70$ cm
iii) $42$cm
iv) $28$ cm

Answer 1

(i) Perimeter of quadrant $=\frac{\pi r}{2}+2r=\frac{22\times 98}{7\times 2}+2\times 98=350cm$

Area of quadrant $=\frac{1}{4}\pi r^2=\frac{1}{4}\times \frac{22}{7}\times 98\times 98=7546{cm}^2$

(ii) Perimeter of quadrant $=\frac{\pi r}{2}+2r=\frac{22\times 70}{7\times 2}+2\times 70=250cm$

Area of quadrant $=\frac{1}{4}\pi r^2=\frac{1}{4}\times \frac{22}{7}\times 70\times 70=3850{cm}^2$

(iii) Perimeter of quadrant $=\frac{\pi r}{2}+2r=\frac{22\times 42}{7\times 2}+2\times 42=150cm$

Area of quadrant $=\frac{1}{4}\pi r^2=\frac{1}{4}\times \frac{22}{7}\times 42\times 42=1386{cm}^2$

(iv) Perimeter of quadrant $=\frac{\pi r}{2}+2r=\frac{22\times 28}{7\times 2}+2\times 28=100cm$

Area of quadrant $=\frac{1}{4}\pi r^2=\frac{1}{4}\times \frac{22}{7}\times 28\times 28=616{cm}^2$